Having said above "Ve'ahavta es Hashem Elokecha", why does the Torah see fit to add "es Hashem Elokecha Tiyra"?
Ramban #1: To deter a person from sinning and getting punished.
Ramban #2: Refer to 6:5:3:2*.
Ramban #3 (citing Temurah, 3b): It is a warning against uttering the Name of Hashem in vain.
Temurah, 4a: It is a warning against uttering the Name of Hashem in vain. 3
What are the connotations of "Oso Sa'avod"?
Ramban #1: It means that one is obligated to serve Hashem like an Eved serves his master.
Ramban #2: It means to serve Hashem by bringing Korbanos 1 in His Name, and by studying His Torah. 2
Ramban #3 (citing the Ibn Ezra): "Es Hashem Elokecha Tiyra" implies not to contravene Mitzvos Lo Sa'aseh, and "Oso Sa'avod", to keeping the Mitzvos Asei. 3
Rashi (in Eikev, 13:5) and Ramban (citing the Sifri) "ve'Oso Sa'avodu" - 'in the Beis-Hamikdash' (Ramban: incorporating Korbanos, singing and bowing, which all fall under the category of Avodah - as the Torah indicates in Bamidbar 18:7, 23').
Ramban, citing the same Sifri.
See Ramban's objection to this explanation.
Since when is it a Mitzvah to swear by Hashem's Name?
Rashi and Ramban #1 (citing the Tanchuma): What the Pasuk means is 1 that if one fears Hashem 2 and serves Him 3 he is permitted to swear by His Name; otherwise, not.
Ramban #2: The Pasuk means that one may only swear by the Name of Hashem, but not by the Name of any other god. 4
Ramban #3 (citing Temurah, 3b), Rosh and Targum Yonasan: The Pasuk is coming to permit swearing by Hashem's Name truthfully. 5
Ramban #4: What the Pasuk means is that Your Yir'as Shamayim will be so deep and you will be dedicated to His service 6 to such an extent, that you will always swear by His Name - even if it is to do something unpleasant - and abide by your oath.
Even though the two preceding statements in the Pasuk are Mitzvos - as the Ramban explains.
Ramban and Rosh: Like Avraham, Yosef and Iyov, who are called 'Yir'ei Elokim'.
Ramban: Someone whose only Avodah is that of Torah and Mitzvos.
Even if it is not for a Mitzvah - See Ramban. See also Peirush Yonasan and Torah Temimah, note 70, who elaborates.
Ramban: To the point that every mundane act that you perform is to serve Hashem - See Ramban DH 'O Yomar'.
Why does the Torah add "u'Bo Sidbak" in Eikev 10:20 and omit it here?
Ba'al ha'Turim: Because there, the Torah mentioned earlier Hashem's love for the Avos, which obligates their descendants to cling to Him.
Panim Yafos #1: Because, whereas in Eikev the Torah is discussing a Shevu'ah that one makes not for a Mitzvah - such as to avoid paying a debt, which is subject to "Bo Sidbak", here it discussing swearing in order to fulfill Mitzvos, which it permits ynconditionally.
Panim Yafos #2: Because, whereas here Moshe is referring to the Dor ha'Midbar all of whom were Chachamim who clung to Hashem 1
